A lot of the times engineers at Google will open source libraries or tools they have worked on, which go under the Google GitHub repo, but are attached with that language. This is basically saying that it is owned by Google but it is not something Google is officially supporting. It may continue to get updates, it may not. I've definitely seen some libraries open sourced from Google, that stopped being pushed externally once the primary driver behind it left Google or moved on to other projects.
You can actually read some of the process that a Googler will follow when open sourcing software here: https://opensource.google/docs/releasing/
That basically goes for Google's official products as well.
Officially supported means it's actually owned by some team. They'll dedicate resources to it, meaning it will be accounted for on any project planning or resource management the management needs to do.
Officially supported things tend to be bigger.
If the project is officially open-sourced, that will be taken into consideration when project priorities, re-orgs, and direction occur at higher levels. "How does this effect our commitment to the community" is a question to address. If it isn't official, then is best-effort by the people who pushed for it to go open-source.
This statement is more like a waiver you'd like to sign while using some entertainment equipements.